How to Determine if a Set of Vectors is Linearly Independent [Passing Linear Algebra]

You see if you can find nonzero weights when writing the zero vector as a linear combination of the vectors in the set.
Interesting Theorem : If a set of vectors contains the zero vector, that set is automatically linearly independent. Why is this? Continue reading:

Think about the linear dependence relation: you pick zeros for all the weights for all the nonzero vectors in the set, but then for the zero vector you can pick ANY NUMBER for its weight and you will get the zero vector as a linear combination. In doing this, you've written a linear combo of the vectors in the set that equals the zero vector, and that one weight was nonzero, right? So, you've done it. The set is linearly dependent bc you can write a linear dependence relation.

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